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M is a decimal such that M = 0.pqrpqrpqrpqr

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M is a decimal such that M = 0.pqrpqrpqrpqr  [#permalink]

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New post 13 Apr 2019, 10:33
4
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

38% (02:24) correct 63% (01:51) wrong based on 24 sessions

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Let the number M be a decimal such that M = 0.pqrpqrpqrpqr… where p, q
and r are digits between 0 & 9. At most two out of p, q and r are equal to 0. By
which of the following should M be multiplied so that it becomes an integer?

A) 99 B) 990 C) 111 D) 1001 E) 3996

Please help.
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M is a decimal such that M = 0.pqrpqrpqrpqr  [#permalink]

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New post Updated on: 16 Apr 2019, 10:05
4
M= 0.PQRPQRPQR... (1)
1000M=PQR.PQRPQRPQR... (2)

(2)-(1)
999M = PQR

So we look for 999 and we dont see a matching answer....Now just multiply both (1) and (2) with 4

4000M = 4*(PQR.PQRPQRPQR...) (3)
4M= 4*( 0.PQRPQRPQR....) (4)

(3)-(4)
3996 M = 4*(PQR) , which is an integer

So, if we multiply M with 3996 we get an Integer
Edit1: So technically any multiple of 999 will be correct. The only option that matches the criteria here is Option E
Hence E. is the correct answer
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Originally posted by saukrit on 13 Apr 2019, 22:09.
Last edited by saukrit on 16 Apr 2019, 10:05, edited 1 time in total.
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Re: M is a decimal such that M = 0.pqrpqrpqrpqr  [#permalink]

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New post 13 Apr 2019, 22:20
Thank you. This really helps. Can you please help me to understand why we are multiplying equation 1 and 2 by 4? Is the strategy used here is to look at the answer options first?
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M is a decimal such that M = 0.pqrpqrpqrpqr  [#permalink]

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New post 13 Apr 2019, 22:28
2
Amrita2405 wrote:
Thank you. This really helps. Can you please help me to understand why we are multiplying equation 1 and 2 by 4? Is the strategy used here is to look at the answer options first?


Since we got to know that by multiplying M with 999 gives us an integer.
Hence, we also know that by multiplying M with 999*N will also give an integer (where N is an Integer)

So technically any multiple of 999 will be correct. The only option that matches the criteria here is Option E.

Hope that helps!!
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M is a decimal such that M = 0.pqrpqrpqrpqr   [#permalink] 13 Apr 2019, 22:28
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